Method of constructing a behavior model of an airplane engine

Abstract

A method of constructing a behavior model (32) of an airplane engine, in particular in order to track the operation of the engine, the method comprising a training step (12) of training at least one statistical regression function on the basis of a generic database (14) containing data from a plurality of airplane engines in order to establish a generic behavior model (10) of the airplane engines, and an additional step of resetting the generic behavior model from data in a database (24) specific to the above-mentioned airplane engine, in order to establish a behavior model (32) that takes account of features specific to that engine.

Claims

1. A method for tracking an operation of an identified airplane engine, the method comprising: acquiring first data from a plurality of airplane engines; storing the first data in a generic database; training at least one statistical regression function in connection with the generic database for establishing a generic behavior model of the plurality of airplane engines; acquiring second data from the identified airplane engine; storing the second data in a specific database specific to the identified airplane engine; resetting the generic behavior model in connection with the second data stored in the specific database for establishing a specific behavior model that takes into account features specific to the identified airplane engine; and tracking the operation of the identified airplane engine based on the specific behavior model, wherein the generic and specific databases include degradation indicators (t) and context variables (v.sub.i), wherein training the at least one statistical regression function further comprises: determining a regression function (f.sub.t) for each context variable (v.sub.i) having an influence on at least one degradation indicator (t) obtained from the generic database, and modeling each degradation indicator (t) by optimizing the regression functions (f.sub.i), wherein resetting the generic behavior model further comprises optimizing each degradation indicator (t) by an additional statistical regression in connection with the specific database for leaving only an affine resetting function as degrees of freedom, and wherein tracking the operation of the identified airplane engine further comprises measuring a value of the degradation indicator (t) and corresponding context variables (v.sub.i) while the identified airplane is in flight, using the additional statistical regression for estimating a value expected for the degradation indicator (t) as a function of the measured corresponding context variables (v.sub.i), and calculating a difference between the expected value for the degradation indicator (t) and the measured value of the degradation indicator (t).

2. The method for tracking according to claim 1, wherein the optimizing is performed by a least squares method.

3. The method for tracking according to claim 1, wherein each regression function (f.sub.i) is a polynomial function.

4. The method for tracking according to claim 1, wherein the measuring, using, and calculating steps are repeated for each flight of the airplane, and wherein the calculated differences are stored in a database and compared with one another for detecting a degradation having an impact on the value expected for the degradation indicator.

5. The method for tracking according to claim 1, wherein the additional statistical regression is a function represented as follows: ${\hat{t}}_{\mathrm{re}\text{-}\mathrm{set}}={}_0+\underset{i=1}{\overset{m}{.Math.}}{}_i{f}_i\left(v_i\right)$ where .sub.0 and .sub.i are constants.

6. The method for tracking according to claim 1, wherein the step of tracking the operation of the identified airplane engine comprises applying said specific behavior model to the identified airplane engine during tracking of starting sequences of the identified airplane engine.

7. A method for tracking an operation of an identified airplane engine, the method comprising: acquiring first data from a plurality of airplane engines; storing the first data in a generic database; training at least one statistical regression function in connection with the generic database for establishing a generic behavior model of the plurality of airplane engines; acquiring second data from the identified airplane engine; storing the second data in a specific database specific to the identified airplane engine; resetting the generic behavior model in connection with the second data stored in the specific database for establishing a specific behavior model that takes into account features specific to the identified airplane engine; and tracking the operation of the identified airplane engine based on the specific behavior model, wherein the generic and specific databases include degradation indicators (t) and context variables (v.sub.i), wherein training the at least one statistical regression function further comprises: determining a regression function (f.sub.i) for each context variable (v.sub.i) having an influence on at least one degradation indicator (t) obtained from the generic database, and modeling each degradation indicator (t) by optimizing the regression functions (f.sub.i), and wherein resetting the generic behavior model further comprises optimizing each degradation indicator (t) by an additional statistical regression in connection with the specific database for leaving only an affine resetting function as degrees of freedom.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) The invention can be better understood and other details, characteristics, and advantages of the invention appear on reading the following description made by way of non-limiting example with reference to the accompanying drawings, in which:

(2) FIG. 1 is a block diagram showing a prior art method of constructing a generic behavior model;

(3) FIG. 2 is a block diagram showing a prior art method of constructing a specific behavior model;

(4) FIG. 3 is a block diagram showing the method of the invention for constructing a generic behavior model that is reset for an engine under consideration;

(5) FIG. 4 is a graph showing how a degradation indicator t.sub.1 varies as a function of a context variable N2.sub.inj, and it comprises three curves respectively showing the regression functions obtained by the generic, specific, and re-set genetic behavior models;

(6) FIG. 5 comprises Tukey box-and-whisker plots showing the distribution of the generic and specific populations, depending on the context variable N2.sub.inj;

(7) FIG. 6 is a graph showing a portion of the curves in the graph of FIG. 4, on a larger scale; and

(8) FIG. 7 is a block diagram showing other steps of the method of the invention for tracking the operation of an airplane engine.

DETAILED DESCRIPTION OF THE INVENTION

(9) FIGS. 1 and 2 show prior art methods of constructing behavior models of airplane engines, these airplane engines being turbine engines such as turboprops or turbojets, for example.

(10) In FIG. 1, a generic behavior model 10 is constructed by training 12 at least one statistical regression function from a generic database 14 containing data coming from a plurality of engines in a fleet.

(11) In FIG. 2, a specific behavior model 20 is constructed by training 22 from at least one statistical regression function on the basis of a database 24 specific to the engine under study.

(12) Nevertheless, those methods suffer from the drawbacks described above.

(13) The method of the invention, as shown diagrammatically in FIG. 3 is based firstly on obtaining a generic behavior model 10 of the above-specified type, but it differs from the method of FIG. 1 in that it also includes a resetting step 30 of resetting this generic model on the basis of data from the database 24 that is specific to the engine under study, in order to establish a re-set behavior model 32 that takes account of specific features of this engine.

(14) The idea is to make use of all of the data from the various engines in a fleet by training a generic regression function. This reveals the physical phenomenon that is taking place, but ignores features specific to the various engines. Thereafter, this generic function is reset specifically on the engine under study, e.g. with the help of new optimization involving only a limited number of parameters and therefore requiring only a small amount of training data. The purpose is to obtain a regression that is more accurate than the generic regression, while being more robust in the face of rare contexts than is the specific regression.

(15) There follows a description of a particular implementation of the method of the invention.

(16) A first step of the method of the invention consists in training the generic regression function.

(17) Initially and for reasons of simplification, it is desired to model a single indicator that is referred to as t, and making use of m context variables written v.sub.1.

(18) For each context variable, with a polynomial regression of order n, a search is made for the regression function having the form:
f.sub.i(v.sub.i)=.sub.i.sup.0+.sub.i.sup.1v.sub.i+.sub.i.sup.2v.sub.i.sup.2+.sub.i.sup.3v.sub.i.sup.3+.sub.i.sup.4v.sub.i.sup.4+ . . . +.sub.i.sup.nv.sub.i.sup.n

(19) Given that there are m context variables for modeling t, there are thus m regression functions f.sub.i.

(20) A conventional ordinary least squares optimization (other methods are also applicable) makes it possible to obtain the coefficients of the regression, which are none other than the coefficients .sub.i.sup.j with i=[1:m] and j=[0:n]. The regression is thus characterized by i*j coefficients.

(21) By way of example, if it is desired to model an indicator by four context variables using a polynomial regression of order 5, a coefficient matrix of size 4*6 is obtained (i.e. having 24 degrees of freedom for the optimization).

(22) It is then possible to estimate the value of the indicator t, as a function of the context variables v.sub.i, as follows:

(23) ${\hat{t}}_{\mathrm{generic}}=\underset{i=1}{\overset{m}{.Math.}}{f}_i\left(v_i\right)$

(24) For this first regression, the training makes use of the generic database containing the data from the different engines (a large database is thus preferred for reasons of robustness). A generic regression function is thus obtained on this database.

(25) Another step of a method of the invention consists in resetting the generic function on the database specific to the engine.

(26) It is now sought to take account of features specific to a particular engine. To do this, a second optimization is performed (e.g. still using ordinary least squares), while leaving only an affine resetting function as degrees of freedom, i.e. for the given indicator t, a function is sought having the form:

(27) ${\hat{t}}_{\mathrm{re}\text{-}\mathrm{set}}={}_0+\underset{i=1}{\overset{m}{.Math.}}{}_i{f}_i\left(v_i\right)$
where beta 0 and beta i are constants.

(28) The new regression may be referred to as a re-set regression.

(29) In the particular example given above, where m=4 and n=5, the resetting is characterized by only five coefficients (one for the additive bias, and four multiplicative coefficients, one per context variable).

(30) A second optimization has thus been performed on the basis of data that is specific to the engine under study, but with many fewer degrees of freedom than were used in the first optimization (about five times fewer in this example).

(31) This makes it possible to retain the general appearance of the generic function (which is very robust), while taking account of the specific features of the engine being modeled.

(32) The person skilled in the art specialized in the technical field in question has sufficient general knowledge to be able to optimize the regression model from a database, as a function of predetermined degrees of freedom.

(33) Once the re-set regression model has been trained, it can be used to eliminate the influence of the context on the indicator and to retain only the impact of the degradation being monitored.

(34) FIG. 7 shows additional steps of the method of the invention for tracking the operation of an engine. The method comprises the additional steps consisting in: measuring the real value of the indicator 40 while the airplane is in flight, together with context variables 42 associated with this indicator; using the re-set regression function 32 for estimating the value expected for the indicator 44 as a function of the measured context variables 42; and calculating the difference 46 between the value expected for the indicator and its measured real value.

(35) The steps can be repeated for each flight, and the calculated differences 46 can be recorded in a database 48 and compared with one another in order to detect any degradation having an effect on the value of the indicator, thereby tracking 50 the operation of the engine.

(36) Reference is made below to FIGS. 4 to 6, which show the advantages of the method of the invention compared with methods of the prior art.

(37) In the example shown, it is desired to model the indicator t1 via the context of variable N2.sub.inj. t1 is the duration of the first stage of starting the engine. This stage begins when the high-pressure spool of the engine begins to rotate, and it terminates when the crew cause fuel to be injected. This instance of injection is identified by the variable N2.sub.inj, which is the speed of rotation of the high-pressure spool during injection. Clearly the later the time when fuel is injected, the longer the duration of the first stage. In other words, the regression function giving t1 as a function of N2.sub.inj is expected to be an increasing function.

(38) FIG. 4 is a graph in which the curves 50, 52, and 54 represent regression functions of the indicator t1 as a function of the variable N2.sub.inj, as established respectively by generic regression (method of FIG. 1), by specific regression (method of FIG. 2), and by reset generic regression (method of the invention as shown in FIG. 3). The graph of FIG. 6 shows a portion of the curves of FIG. 4 on a larger scale over the range 25% to 30% of N2 for N2.sub.inj.

(39) FIG. 5 comprises Tukey box-and-whisker plots showing the distributions of the generic and specific populations (top and bottom plots) as a function of the variable N2.sub.inj.

(40) It can be seen that the re-set regression 54 conserves the general shape of the generic regression 50. It therefore benefits from the robustness properties of the generic regression over contexts that are rare (N2.sub.inj<25% and N2.sub.inj22 31%). Its range of validity is therefore extended compared with the specific regression 52.

(41) Furthermore, the re-set regression 54 comes close to the specific regression 52 over the portion that is populated by the specific database (25%<N2.sub.inj<30%cf. FIG. 6). Some of the specific features of the engine under study are thus taken into account.